Classical single-test Bayesian optimization works by updating an acquisition function, \(\alpha (D)\in \mathbb {R}^n\) , at each stage and then sampling the candidate that maximizes it. See [1]} for an introduction. Note that in the case of single-test Bayesian optimization there are only two sets of candidates of interest: the untested candidates \(I_{\hbox{u}}\)  and the tested candidates \(I_{\hbox{t}}\) . See Algorithm .
